Question

Q29) Find the area of a trapezium whose parallel sides are 25cm, 13cm and other non
parallel sides are 15cm each.

Answer 1

Answer:

57√21 cm²

Step-by-step explanation:

Given : AB = 13 cm

CD = 25 cm

AD = BC = 15 cm

To Find : Area of Trapezium ABCD

Solution : In trapezium ABCD

DE + EF + FC = CD

Putting known values, we get

→ DE + 13 + FC = 25 (AB = EF = 13 cm)

→ DE + FC = 25 - 13

→ DE + FC = 12

Both DE and FC are equal in magnitude as the non - parallel sides are equal.

So, DE = FC = 12/2 = 6 cm

Now,

In ∆ AED, ∠AED = 90°, applying Pythagoras Theorem, we get

→ (AD)² = (AE)² + (DE)²

→ (15)² = (AE)² + (6)²

→ 225 = (AE)² + 36

→ (AE)² = 225 - 36

→ (AE)² = 189

→ AE = √189

→ AE = √(3 × 3 × 3 × 7)

→ AE = 3√21 cm

Now,

Area of Trapezium = 1/2 × Sum of Parallel sides × Height

= 1/2 × (13 + 25) × 3√21

= 1/2 × 38 × 3√21

= 19 × 3√21

= 57√21 cm²